Fixed effects analysis of repeated measures data.

The analysis of repeated measures or panel data allows control of some of the biases which plague other observational studies, particularly unmeasured confounding. When this bias is suspected, and the research question is: 'Does a change in an exposure cause a change in the outcome?', a fixed effects approach can reduce the impact of confounding by time-invariant factors, such as the unmeasured characteristics of individuals. Epidemiologists familiar with using mixed models may initially presume that specifying a random effect (intercept) for every individual in the study is an appropriate method. However, this method uses information from both the within-individual/unit exposure-outcome association and the between-individual/unit exposure-outcome association. Variation between individuals may introduce confounding bias into mixed model estimates, if unmeasured time-invariant factors are associated with both the exposure and the outcome. Fixed effects estimators rely only on variation within individuals and hence are not affected by confounding from unmeasured time-invariant factors. The reduction in bias using a fixed effects model may come at the expense of precision, particularly if there is little change in exposures over time. Neither fixed effects nor mixed models control for unmeasured time-varying confounding or reverse causation.